XDI analysis of Mutual-Exclusion Element

Processing AND/IF input stream:
-----------------------------------------------------------------------------
  1> (AND/IF_1.0
  2>   (NFA
  3>     (NAME Mutual-Exclusion Element)
  4>     (SYMBOLS 
  5>       (r0 INPUT) (a0 OUTPUT) (r1 INPUT) (a1 OUTPUT)
  6>     )
  7> 
  8>     (STATES
  9>       (0 INITIAL BOX)
 10>       (1 TRANSIENT)
 11>       (4 TRANSIENT)
 12>       (2 BOX)
 13>       (5 TRANSIENT)
 14>       (3 TRANSIENT)
 15>       (6 BOX)
 16>       (7 TRANSIENT)
 17>       (8 BOX)
 18>       (9 BOX)
 19>       (10 TRANSIENT)
 20>       (11 TRANSIENT)
 21>       (12 TRANSIENT)
 22>       (14 TRANSIENT)
 23>       (13 TRANSIENT)
 24>     )
 25>     (TRANSITIONS
 26>       (0 1 r0) (0 4 r1)
 27>       (1 2 a0) (1 5 r1)
 28>       (4 5 r0) (4 8 a1)
 29>       (2 3 r0) (2 6 r1)
 30>       (5 6 a0) (5 9 a1)
 31>       (3 0 a0) (3 7 r1)
 32>       (6 7 r0)
 33>       (7 4 a0) (7 10 a1)
 34>       (8 9 r0) (8 11 r1)
 35>       (9 12 r1)
 36>       (10 8 a0) (10 14 r1)
 37>       (11 12 r0) (11 0 a1)
 38>       (12 13 a0) (12 1 a1)
 39>       (14 11 a0) (14 3 a1)
 40>       (13 14 r0) (13 2 a1)
 41>     )
 42>   )
 43> )
-----------------------------------------------------------------------------

Mutual-Exclusion Element: warning: interpretation not given. Assuming 'Verhoeff/XDI'
Mutual-Exclusion Element: 1 warning, 0 errors.

Statistics

4 symbols:

2 input and 2 output

15 states:

0 demanding, 5 indifferent and 10 transient

28 transitions:

14 input and 14 output

Automorphisms (symmetries)

There are 2 automorphisms.

Finest Semi-independent Partition

/ r0 a0 / r1 a1 /

Choice, Order Dependence, Nondeterminism

• Maximally Transient
• No Disabling Inputs (Z^inp)
• Disabling outputs (Z^out) in state(s):

  5

• Order-Independent input (Y^inp)
• Order-Independent output (Y^out)
• Output refusal sets do NOT propagate backward over inputs in state(s):

  1 4

• Output Non-Deterministic

Distances

All states are reachable from the initial state:
[ + == 9 < distance < +inf , . == distance = +inf ]

											1	1	1	1	1
	0	1	4	2	5	3	6	7	8	9	0	1	2	4	3
0:	0	1	1	2	2	3	3	4	2	3	5	3	4	6	5

Initial state reachable from all states.
All states reachable from all other states.

Shortest paths from initial state:

0:
1:	r0
4:	r1
2:	r0 a0
5:	r0 r1
3:	r0 a0 r0
6:	r0 a0 r1
7:	r0 a0 r0 r1
8:	r1 a1
9:	r0 r1 a1
10:	r0 a0 r0 r1 a1
11:	r1 a1 r1
12:	r0 r1 a1 r1
14:	r0 a0 r0 r1 a1 r1
13:	r0 r1 a1 r1 a0

Distribution of distances from initial state:
[d=distance, h=occurrence count, c=cumulative occurrence count]

d:	h	[ c]
0:	1	[ 1]
1:	2	[ 3]
2:	3	[ 6]
3:	4	[10]
4:	2	[12]
5:	2	[14]
6:	1	[15]

Autocomparison Matrix

There are no state pairs (x,y) where x refines y outside the diagonal.

XDI Validity

'Mutual-Exclusion Element' is a valid XDI specification.